Abstract
The evaluation of generic Cachazo-He-Yuan(CHY)-integrands is a big challenge and efficient computational methods are in demand for practical evaluation. In this paper, we propose a systematic decomposition algorithm by using cross-ratio identities, which provides an analytic and easy to implement method for the evaluation of any CHY-integrand. This algorithm aims to decompose a given CHY-integrand containing higher-order poles as a linear combination of CHY-integrands with only simple poles in a finite number of steps, which ultimately can be trivially evaluated by integration rules of simple poles. To make the method even more efficient for CHY-integrands with large number of particles and complicated higher-order pole structures, we combine the Λ-algorithm and the cross-ratio identities, and as a by-product it provides us a way to deal with CHY-integrands where the Λ-algorithm was not applicable in its original formulation.
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Cardona, C., Feng, B., Gomez, H. et al. Cross-ratio identities and higher-order poles of CHY-integrand. J. High Energ. Phys. 2016, 133 (2016). https://doi.org/10.1007/JHEP09(2016)133
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DOI: https://doi.org/10.1007/JHEP09(2016)133